Question: Solve for $x$ and $y$ using substitution. ${x-5y = -5}$ ${x = y+3}$
Solution: Since $x$ has already been solved for, substitute $y+3$ for $x$ in the first equation. ${(y+3)}{- 5y = -5}$ Simplify and solve for $y$ $y+3 - 5y = -5$ $-4y+3 = -5$ $-4y+3{-3} = -5{-3}$ $-4y = -8$ $\dfrac{-4y}{{-4}} = \dfrac{-8}{{-4}}$ ${y = 2}$ Now that you know ${y = 2}$ , plug it back into $\thinspace {x = y+3}\thinspace$ to find $x$ ${x = }{(2)}{ + 3}$ ${x = 5}$ You can also plug ${y = 2}$ into $\thinspace {x-5y = -5}\thinspace$ and get the same answer for $x$ : ${x - 5}{(2)}{= -5}$ ${x = 5}$